Question

what are the domain and range of f(x) = 4x – 8? domain: {x | x is a real number}; range: {y | y > –8} domain: {x | x is a real number}; range: {y | y > 8} domain: {x | x > 4}; range: {y | y > –8} domain: {x | x > –4}; range: {y | y > 8}

Answer 1

Answer : domain: {x | x is a real number}; range: {y | y >- 8}

the domain and range of $f(x) = 4^x – 8$

For exponential function , there is no restriction for x

So domain is all real numbers

For exponential function , $f(x) = a^x + b$

The range is y > b

The range of $f(x) = 4^x -8$ is y> -8

domain: {x | x is a real number}; range: {y | y > –8}

Answer 2

The domain and range of f(x) = 4ˣ – 8 are :

domain: {x | x is a real number}

range: {y | y > –8}

Further explanation

Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.

There are many types of functions in mathematics such as :

• Linear Function → f(x) = ax + b

• Quadratic Function → f(x) = ax² + bx + c
• Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x
• Logarithmic function → f(x) = ln x
• Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...

If function f : x → y , then inverse function f⁻¹ : y → x

Let us now tackle the problem!

Given :

$f(x) = 4x - 8$

The function above is called a linear function that has a general form:

$\boxed {f(x) = ax + b}$

Domain for all of linear function is always = { x | x is a real number }

The value of f(x) = 4x - 8 for x is a real number will also be a real number , so :

Range for f(x) will be = { y | y is a real number }

The answer above is not available in the multiple choices, so the problem is different from what was written above.

Let's assume the function is f(x) = 4ˣ - 8

The function above is called exponential function that has a general form:

$\boxed {f(x) = a.b^x + c}$

Domain for this function should be { x | x is a real number }

If x < 0 , then the minimum value of f(x) will approach -8

Range for this function will be { y | y > -8 }

Example :

x = -1 → y = 4⁻¹ - 8 = -7.75

x = -4 → y = 4⁻⁴ - 8 = -7.996

x = -10 → y = 4⁻¹⁰ - 8 = -7.9999

The graph of the two functions above can be seen in the attachment.

Learn more

• Inverse of Function : https://brainly.com/question/9289171
• Rate of Change : https://brainly.com/question/11919986
• Graph of Function : https://brainly.com/question/7829758

Answer details

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic